SANAA, Yemen — Hundreds of thousands of Yemenis protested in several major cities on Tuesday, demanding that embattled President Ali Abdullah Saleh and his relatives face trial and calling for the creation of a transitional presidential council to run this poor but strategic Middle Eastern nation.

The protests were the largest since Saleh flew to neighboring Saudi Arabia for medical treatment for severe injuries sustained in a June 3 attack on his presidential compound. The demonstrators are seeking to take advantage of Saleh’s absence to install a new government that would end his nearly 33-year rule.

In addition to political paralysis, the nation is reeling from shortages of fuel, electricity and water as government forces are engaged in an intensifying struggle with Islamist militants, many with links to al-Qaeda’s Yemen branch, who have taken over large swaths of territory in southern Yemen.

Early Wednesday, the Associated Press reported that Islamist militants carried out a surprise dawn atatck on Houta, the capital of the southern Lahj province, and seized several neighborhoods of the city. Bands of militants, suspected to be linked to al-Qaeda, also drove through the port city of Aden, opening fire at security forces, officials told the AP. In late May, militants seized the towns of Zinjibar and Jaar in Abyan province.

On Tuesday, thousands of protesters in the capital, Sanaa, marched toward the residence of Vice President Abed Rabbo Mansour Hadi, the acting head of state, demanding that he stand with the populist uprising and create the council.

“We are here to demand an immediate establishment of a transitional governing council to run the country,” said Maha Naji, a protester, adding that Saleh and others who commanded government forces that killed protesters at recent anti-government demonstrations should face justice. “We want the prosecution of those who are killing the people.”

The growing pressure from Yemen’s streets follows talks between Hadi and political opposition groups on Monday to break the political impasse and pave the way to a gradual handover of power. But the youth activists want to start a new political era and are demanding that all of Saleh’s loyalists leave the government.

In a statement, youth leaders said they rejected any dialogue with “the remnants of the Saleh regime” and would consider any agreement that includes them as “illegitimate.”

The protests unfolded in several places across the country, from Hadramawt in the east to Saada in the north. In Taiz, Yemen’s second-largest city and a nexus of the uprisings, protesters clashed with military units guarding the city’s presidential palace. There were no reports of casualties.

U.S. officials expressed concern Tuesday that the al-Qaeda affiliate in Yemen could further enhance its abilities to target the United States and its allies.

Daniel Benjamin, a top State Department counterterrorism official, told reporters that Washington is worried that the unrest could lead to stronger ties between al-Qaeda’s Yemen branch and Somalia’s al-Shabab militia, also linked to al-Qaeda. Somalia and Yemen are separated only by a stretch of sea, with either shore easily reachable by boat.